A reliable transmission with QoE (Quality of Experience) guarantee is crucial for internet conversational service applications. However, due to the limited network bandwidth bottleneck effect and the drawback of transmission technology, there exists no mature and open QoE technical solution for this service. In this paper, we focused our attention on a load distribution strategy for multipath relay transmission to meet the QoE requirements of conversational real-time HD video services. It consisted of three stages: First, a series of relay nodes was deployed in the backbone network, and a software defined overlay network was constructed to perform the multipath relay transmission for the service. Second, by an analysis of the QoE feature, a bijection was built for each quantitative QoE and its MOS (Mean Opinion Score) score. Finally, considering the influence of the coupling relation between paths on the service quality in multipath relay transmission, fuzzy cooperative game theory was used to design the service load distribution strategy. Many experiments showed that compared with state-of-the-art methods in the single-path transmission scene, the strategy we designed can dynamically adjust the load distribution of each sub-path according to the change in QoS (Quality of Service) information of the transmission path in real time. While meeting the strict real-time constraints of the service, it can effectively avoid the impact of network random congestion on the service QoE.